As semiconductor geometries continue to shrink, manufacturers have increasingly turned to optical techniques to perform non-destructive inspection and analysis of semiconductor wafers. Optical techniques typically apply an incident field (often referred to as a probe beam) to a sample and then detect and analyze the reflected energy. This type of inspection and analysis is known as optical metrology and is performed using a range of optical techniques. Scatterometry is a specific type of optical metrology that is used when the structural geometry of a sample creates diffraction (optical scattering) of the incoming probe beam. Scatterometry systems analyze diffraction to deduce details of the structures that cause the diffraction to occur.
Various optical techniques have been used to perform optical scatterometry. These include broadband spectroscopy (U.S. Pat. Nos. 5,607,800; 5,867,276 and 5,963,329), spectral ellipsometry (U.S. Pat. No. 5,739,909) single-wavelength optical scattering (U.S. Pat. No. 5,889,593), and spectral and single-wavelength beam profile reflectance and beam profile ellipsometry (U.S. Pat. No. 6,429,943). In addition it may be possible to employ single-wavelength laser BPR or BPE to obtain critical dimension (CD) measurements on isolated lines or isolated vias and mesas. The above cited patents and patent applications, along with U.S. Pat. Nos. 6,704,661, 6,819,426, 6,813,034,U.S. Patent Publication No. 2001/0051856 A1, U.S. Pat. Nos. 6,694,275, 6,483,580, 7,099,005, and U.S. Patent Publication No. 2004/0070772, all of which are incorporated herein by reference.
A typical scatterometry system includes an illumination source that creates a mono or polychromatic probe beam. The probe beam is preferably focused by one or more optical components to create an illumination spot on the surface of the sample under test. A second series of optical components transports the diffracted probe beam to a detector. The detector captures the diffracted energy and produces corresponding output signals. A processor analyzes the signals generated by the detector.
In most cases, a modeling process is used to translate the empirical measurements obtained during scatterometry into physical measurements such as line widths. For this process, a software model is used to represent the expected structure and composition of the sample. The software model is parameterized, allowing characteristics such as line widths and line profiles to be changed. Maxwell's equations are used to predict the diffraction that the modeled structure would impart to the probe beam of the scatterometer. A set of these predicted measurements are generated using variations to the parameters of the model. This process is repeated until the predicted measurements match the empirical measurements to a desired goodness of fit. At that point, the modeled structure and its associated parameters are assumed to match the sample. The predictions can be calculated in advance and stored in a library or calculated in real time (or using some combination of both approaches as is known by one skilled in the art).
To be accurate, the model used during the modeling process must reflect the structure and composition of the sample. Complex samples require correspondingly complex modeling techniques. For one of these techniques, a Riemannian approach is used to model geometric shapes (such as the lines) as stacks of slabs. The height and width of each slab is chosen so that the stack of slabs approximates the shape being modeled. Portions of the shape that change rapidly can be accurately modeled by increasing the number of slabs while decreasing their thickness. Shape portions that are relatively constant may be modeled using fewer, thicker slabs. Models constructed using this technique require two parameters for each slab (height, width) or a total of 2N parameters for N slab models.
The slab-based technique necessarily introduces a degree of roughness into the resulting model. This roughness gives the model edges a staircase-like appearance attributable to the rectangular cross-section of the individual slabs. This side effect can be reduced by using slabs that have a trapezoidal cross-sections or quadrilateral cross-sections. The overall effect is a reduction in stair-stepping at the cost of additional parameters. For trapezoidal cross-sections, three parameters are required for each slab (height, width and one interior angle). Quadrilateral cross-sections require four parameters (height, width and two interior angles).
Quadrilaterals or trapezoids are an effective method for increasing the accuracy of the modeling process. At the same time, the increased number of parameters adds further complexity to an already arduous computational process. As a result, there are continuing efforts to find modeling methods that provide high accuracy while limiting the number of required parameters. This is the goal of the method described, for example in U.S. Pat. No. 5,963,329 (incorporated herein by reference). For this method, the familiar slab-based approach is used to model lines and other geometric shapes. In this case, however, the slabs are subdivided into one or more sub-profiles. Each sub-profile has a reference edge and a reference height. The width of each slab in a sub-profile is defined using an offset (which may be positive or negative) from the reference edge. The height of each slab in a sub-profile is defined as a multiple of the reference height. Each sub-profile also has two scaling factors, one for height and a second for width. Changing the height scaling factor increases or decreases the height of all of the slabs in a sub-profile making the sub-profile taller or shorter. Changing the width scaling factor spreads the sub-profile-slabs that are narrower than the reference edge become narrower still, slabs that are wider than the reference edge become even wider. By controlling the scaling factors for each sub-profile, the overall profile of the line can be varied to produce a range of differing shapes.
The use of sub-profiles and associated scaling factors decreases the number of parameters that are required to define a particular shape. Unfortunately, the use of rectangular slabs suffers from the staircase limitations already described. It is also true that the use of scaling factors is only beneficial when computational results can be re-used as the scaling factors are changed. For cases where this is not possible, the use of scaling factors is computationally similar to more traditional methods for defining slab heights and widths.
Other approaches have been disclosed for generating a model that defines the shape and material properties of the sample. For example, in the above cited U.S. Pat. No. 6,704,661, a method is disclosed wherein an initial model is defined as having a rectangular shape. The optical response of the rectangle is iteratively calculated as the height and width parameters are modified. Once a best fit has been achieved, a new model is created by modifying the optimized rectangle with more than one width and more than one layer. The fitting process is repeated and then further widths and layers are added. This process is continued until the optical response of the model matches the measured data to a predetermined level of fitness.
More recently, the assignee herein developed yet another modeling approach which is described in U.S. Pat. No. 7,145,664, incorporated herein by reference. In this global shape definition technique, a control-point based approach is used to define the geometric shapes within samples. As an example, consider the case of a sample that includes one or more lines. The profile (i.e., the cross-sectional outline) of a representative line is defined using a set of control points. Each control point influences the shape of the line profile. For some cases, this means that control points define shapes in a connect-the-dots fashion. For other cases, a more complex mathematical function, such as Bezier or Spline curve fitting, is used to translate a set of control points into a corresponding shape. It should be noted that the control points are preferably only used to define shapes. Layers within a shape can be modeled independently. An interactive environment allows a user to specify multilayer scatterometry models with single periodicity. The user can add shape profiles by adding groups of control points.
All of the above described techniques have been implemented to evaluate samples having structural features which repeat in a uniform fashion. More recently, samples of interest have become more complex. These samples have a first region where the layer structures repeat with a first periodicity. The samples also have a second region, added on top of the first region, where the layer structures repeat with a different periodicity. Attempting to model these complex multi-periodic samples is difficult. This disclosure addresses this problem.